An airplane flight from Houston, Texas to Rome, Italy is 5,686 miles. Estimate the distance between the two cities as the product of a single digit number times a power of 10.(1 point) Responses 5×103 5 times 10 cubed 6×104 6 times 10 to the 4th power 5×104 5 times 10 to the 4th power 6×103
To estimate the distance between Houston and Rome as the product of a single-digit number times a power of 10, we need to move the decimal point of 5,686 to the left until we get a new number between 1 and 10.
Starting from 5,686, we move the decimal point 3 places to the left to get 5.686.
However, we need to multiply this new number by 10 raised to the power of 3, since we moved the decimal point 3 places to the left.
So the estimate of the distance between Houston and Rome is 5.686 × 10^3, which can also be written as 5×10^3.
Therefore, the correct response is 5×10^3.